Programs in Physics & Physical Chemistry
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|Manuscript Title: New efficient programs to calculate general recoupling coefficients. Part II: evaluation of a summation formula.|
|Authors: V. Fack, S.N. Pitre, J. Van der Jeugt|
|Program title: NJSUMMATION, NJSUMPAR|
|Catalogue identifier: ADBA_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 86(1995)105|
|Programming language: C.|
|Computer: 386/486-BASED PCs.|
|Operating system: MS-DOS, LINUX, UNIX.|
|Keywords: Atomic structure, Nuclear structure, General purpose, Scattering, General recoupling Coefficient, Angular momentum, Racah coefficient, 3n-j coefficient, Recursive techniques, Arbitrary nested loops, Parallel processing, Transputer, Farming technique, Rotation group.|
Nature of problem:
A general recoupling coefficient for an arbitrary number of (integer or half-integer) angular momenta can be expressed as a formula consisting of products of 6-j coefficients summed over a certain number of variables. Such a formula can be generated using the program NJFORMULA . The present programs perform the evaluation of a generated formula for given data of angular momenta.
A summation formula for a general recoupling coefficient can contain an arbitrary number of summation variables, which is determined by the binary trees involved in the search process when generating the formula . To develop a general algorithm for the evaluation of such a formula, we use recursive programming techniques which allow to implement arbitrary nested loops. Apart from the sequential implementation NJSUMMATION of this algorithm, we also present a parallel version NJSUMPAR, which can be executed on a network of transputers. The latter uses a farming technique, where a master processor distributes work packets to several worker processors who calculate products of 6-j coefficients.
For the sequential program the running time is determined mainly by the number of 6-j coefficients computed in the evaluation process. Typical examples, involving up to ten thousand 6-j coefficients, take less than 0.25 seconds on the Sun Sparc, less than 0.5 seconds on the 486-based PC, and less than 50 seconds on a single T800 transputer. More complicated examples, involving up to one million 6-j coefficients, take less than 20 seconds on the Sun Sparc and less than 40 seconds on the 486-based PC. For the parallel program we focus our attention on the advantage factor of the parallel version compared with the sequential version. On a network of 4 transputers, the parallel program is 3 to 4 times faster than the corresponding sequential version.
|||V. Fack, S.N. Pitre, J. Van der Jeugt, Comp. Phys. Commun. 83(1994)275.|
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